mean

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Mean

The expected value of a random variable. Arithmetic average of a sample.

Arithmetic Mean Average

An average calculated by adding the value of the points in a data set and dividing the sum by the number of data points. For example, suppose one wishes to calculate the average income of a country with exactly five people in it, and their incomes are $25,000, $26,000, $43,000, $70,000, and $72,000. It is calculated as:

($25,000 + $26,000 + $43,000 + $70,000 + $72,000) / 5 = $47,200.

A limitation to the arithmetic mean average is that it can be overly affected by extremes in either direction. For example, if one of the five persons in the country earns $100 billion per year, the arithmetic mean average income would be in the billions and would not accurately count the other four citizens. For this reason, many analysts use the median in conjunction with the arithmetic mean average. The arithmetic mean average is also called simply the mean.

mean

The average of a set of numbers.Contrast with median,which is the middle figure in a set of numbers,and mode,which is the value that appears most often in a set of numbers.

Example: A survey of home values in a neighborhood of nine houses obtained the following values:

The mean, or average, is the total of all values divided by 9, or $143,044.The median is the middle number when the numbers are all arranged from highest to lowest,which would be house 5, or $139,850.The mode is $139,000,because it is the number that appears most often.

References in periodicals archive ?
Then we update x by replacing its outlying components with the corresponding mean components from the mean vector [[mu].sub.k,[beta]] of kth population.
The covariance matrices [[SIGMA].sub.n] are initially identity matrices, while the choice of mean vectors [[mu].sub.n] is made by a k-means clustering, where k-means clustering chooses the mean vectors randomly [19].
Each datum is then assigned to the cluster with the nearest mean vector.
It is well known that the sample mean vector and covariance matrix ([??] and S) are not resistant to the effects of even a single outlying value in the data [6].
is the between-class scatter matrix, and m = 1/25 [SIGMA]x = 1/25 [[summation].sup.5.sub.k=1] 5[m.sub.k] is the mean vector of all training samples, while
which we recognize as the sum of squares of normalized scores calculated from the vector of differences between each individual observation [Y.sub.ki] and the subgroup mean vector [[bar.Y].sub.k].
In the proposed system, for each letter population, we calculate the mean vector for that population (4), which defines the codeword associated with that letter.
However, if the mean vector exists, it will be E(X) = [mu], and if the covariance matrix exists, it will be
where [y.sub.k] [member of] [R.sup.m] is a centralized feature vector and [mu] [member of] [R.sup.n] is the mean vector of all the sample vectors, while W [member of] [R.sup.nxm] is a transform matrix with orthonormal column vectors.
The null hypothesis of mean vector equality associated with the scenarios using aggregate soil loss variables was strongly rejected across all comparisons (Table 4).
where x = ([x.sub.1],..., [x.sub.M])', [mu] = ([[mu].sub.1],..., [[mu].sub.M])' is the mean vector, and [SIGMA] = [[[sigma].sub.ij]] is the positive definite covariance matrix.
, [y.sub.p], [mu], [SIGMA]) is normally distributed with mean vector [??] and covariance matrix [??].